Y. Komori and K. Burrage (2012), Weak second order S-ROCK methods for Stratonovich
stochastic differential equations, Journal of Computational and Applied
Mathematics, 236 (11), 2895-2908.
Abstract
It is well known that the numerical solution of stiff stochastic ordinary
differential equations leads to a step size reduction when explicit methods
are used. This has led to a plethora of implicit or semi-implicit methods
with a wide variety of stability properties. However, for stiff stochastic
problems in which the eigenvalues of a drift term lie near the negative
real axis, such as those arising from stochastic partial differential equations,
explicit methods with extended stability regions can be very effective.
In the present paper our aim is to derive explicit Runge-Kutta schemes
for non-commutative Stratonovich stochastic differential equations, which
are of weak order two and which have large stability regions. This will
be achieved by the use of a technique in Chebyshev methods for ordinary
differential equations.
Note
The journal is abstracted/indexed in MathSciNet and Web of Science. Thus, additional information about the paper is obtainable from the databases.
The pdf file is obtainable from here. (Access to the file will depend on your entitlements.)
The following are source files implimenting the algorithm proposed in the paper:
Last updated: 2012/11/21